PolygonCoordinates [poly]
gives a list of coordinates in the polygon poly.
PolygonCoordinates
PolygonCoordinates [poly]
gives a list of coordinates in the polygon poly.
Details
- PolygonCoordinates is also known as polygon vertex coordinates.
- PolygonCoordinates is defined by the canonicalization performed in CanonicalizePolygon .
- PolygonCoordinates gives a list of coordinates {p1,p2,…}.
- For a polygon with self-intersections, the resulting coordinate list will also include intersection points.
- For a polygon defined with repeated coordinates, the resulting coordinate list removes duplicate coordinates.
Examples
open all close allBasic Examples (1)
Get the vertex coordinates from a Polygon :
𝒫 = Polygon[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {1, 2, 3, 4}];PolygonCoordinates[𝒫]Graphics[𝒫]Scope (6)
PolygonCoordinates works on polygons:
Polygon[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {1, 2, 3, 4}];PolygonCoordinates[%]Triangle:
PolygonCoordinates[Triangle[]]Graphics[Triangle[]]Rectangle:
PolygonCoordinates[Rectangle[]]PolygonCoordinates works on polygons of geographic entities:
PolygonCoordinates[Polygon[["france"]]]//Short[#, 2]&Polygons with GeoPosition :
Polygon[GeoPosition[{{{40.083441, -88.235716}, {40.083607, -88.257488}, {40.082603, -88.257149},
{40.076136999999996, -88.25740499999999}, {40.076178, -88.270888}, {40.076516, -88.271558},
{40.083686, -88.271512}, {40.083659999999995, -88.267046}, ... 33323}, {40.098112, -88.228687},
{40.095216, -88.228627}, {40.095179, -88.238547}, {40.094480999999995, -88.238546},
{40.094508999999995, -88.23267}, {40.094106, -88.232556}, {40.090666999999996, -88.232477},
{40.090741, -88.235745}}}]];PolygonCoordinates[%]//Short[#, 2]&Polygons with GeoPositionXYZ :
Polygon[GeoPositionXYZ[{{{150451.6968462432, -4.884430486484052*^6, 4.085078564164219*^6},
{148595.27532671497, -4.884475441490381*^6, 4.085092666620835*^6},
{148626.35829777512, -4.884546311005128*^6, 4.0850073717259285*^6},
{148618.5908634042 ... 7*^6, 4.0860187668081024*^6},
{150697.56410771207, -4.8836599487428395*^6, 4.085984535480795*^6},
{150711.88303095422, -4.883905546449982*^6, 4.0856924143435075*^6},
{150433.15479548014, -4.883908845676418*^6, 4.0856987003255524*^6}}}]];PolygonCoordinates[%]//Short[#, 2]&Polygons with GeoPositionENU :
Polygon[GeoPositionENU[{{{3378.2547059731055, -3369.2234780923936, -0.7440009205072329},
{1521.3211635380246, -3351.391253626573, -0.022340134218666208},
{1550.2571145363192, -3462.8657556618973, -0.08899812728964207},
{1528.5672303494055, -418 ... 63383291193, -0.37494203351275246},
{3654.121991908476, -2566.7472331234085, -0.5214977847472255},
{3375.420726854886, -2558.6597093173914, -0.3648706331350695}}},
GeoPosition[{40.11379115639895, -88.2753251202516, -1.0415787873318691}]]];PolygonCoordinates[%]//Short[#, 2]&PolygonCoordinates works on polygons with GeoGridPosition :
Polygon[GeoGridPosition[{{{-0.9950503945490105, 1.2366760550756015},
{-0.9952074890903578, 1.2369207053693891}, {-0.9952196732768064, 1.2369073327446167},
{-0.9953160063787643, 1.236848436956935}, {-0.9954141759436825, 1.2369993898475449},
{-0. ... 197645333103}, {-0.9949098578570917, 1.2368130881428654},
{-0.9948663952535768, 1.2367477711687371}, {-0.9948714472169538, 1.2367426500757825},
{-0.9949211061652593, 1.2367089232486177}, {-0.9949439717990124, 1.236746107097628}}}, "Bonne"]];PolygonCoordinates[%]//ShortPolygon with holes:
Polygon[{{0, 0}, {3, 0}, {3, 3}, {0, 3}, {1, 1}, {1, 2}, {2, 2}, {2, 1}}, {1, 2, 3, 4} -> {{5, 6, 7, 8}}];PolygonCoordinates[%]Polygons with disconnected components:
Polygon[{{0, 0}, {1, 0}, {0, 1}, {1, 1}, {2, 1}, {1, 2}}, {{1, 2, 3}, {4, 5, 6}}];PolygonCoordinates[%]Polygons in :
Polygon[{{2, 3, 1, 0}, {6, 9, 1, 0}, {5, 4, 1, 0}, {8, 2, 1, 0}}, {1, 2, 3, 4}];PolygonCoordinates[%]Properties & Relations (3)
Using CanonicalizePolygon to get polygon coordinates:
𝒫 = Polygon[{{0, 0}, {1, 0}, {0.5, 0.8}}];First[CanonicalizePolygon[𝒫]]PolygonCoordinates[𝒫]Using MeshCoordinates to get polygon coordinates:
𝒫 = Polygon[{{0, 0}, {1, 0}, {0.5, 0.8}}];mesh = BoundaryDiscretizeRegion[𝒫, MaxCellMeasure -> 1]MeshCoordinates[mesh]PolygonCoordinates[𝒫]A simple polygon has the same polygon coordinates as its OuterPolygon :
𝒫 = Polygon[{{0.016027421699362776, 0.276831297955467}, {0.5077817136202725, 0.023714305171669503},
{0.883435505999971, 0.37966194313367274}, {0.8136436053400857, 0.6761206348576514},
{0.9500797352424271, 0.9350184461840005}}, {1, 2, 3, 4, 5}];SimplePolygonQ[𝒫]PolygonCoordinates[𝒫]PolygonCoordinates[OuterPolygon[𝒫]]Related Guides
History
Text
Wolfram Research (2019), PolygonCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/PolygonCoordinates.html.
CMS
Wolfram Language. 2019. "PolygonCoordinates." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolygonCoordinates.html.
APA
Wolfram Language. (2019). PolygonCoordinates. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolygonCoordinates.html
BibTeX
@misc{reference.wolfram_2026_polygoncoordinates, author="Wolfram Research", title="{PolygonCoordinates}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonCoordinates.html}", note=[Accessed: 14-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_polygoncoordinates, organization={Wolfram Research}, title={PolygonCoordinates}, year={2019}, url={https://reference.wolfram.com/language/ref/PolygonCoordinates.html}, note=[Accessed: 14-August-2026]}